Reliable A Posteriori Error Estimator for a Multi-scale Cancer Invasion Model

TL;DR

This paper develops and tests a residual-based a posteriori error estimator for a complex multi-scale cancer invasion model, demonstrating its reliability and efficiency in three-dimensional simulations.

Contribution

It introduces a novel residual-based error estimator tailored for a multi-scale cancer invasion model, with validation through computational experiments.

Findings

The error estimator is reliable across small perturbation parameters.

The estimator performs efficiently in 3D numerical tests.

It improves error control in finite element approximations.

Abstract

In this work, we analyze the residual-based a posteriori error estimation of the multi-scale cancer invasion model, which is a system of three non-stationary reaction-diffusion equations. We present the numerical results of a study on a posteriori error control strategies for FEM approximations of the model. In this paper, we derive a residual type error estimator for the cancer invasion model and illustrate its practical performance on a series of computational tests in three-dimensional spaces. We show that the error estimator is reliable and efficient regarding the model's small perturbation parameters.